Why does turbo tax app say my federal return was accepted, but the IRS says my return was received?

It does mean the same. Accepted or Received means your return was received and the basics (such as the correct social security number) seem to be in order.

• Once the IRS takes a deeper look, they will (hopefully) quickly approve your refund. For more details on their process, see: Does accepted mean my refund is approved?

To track your federal refund, look on the IRS Where's My Refund site. 

For state refunds, use your state government's refund lookup service.

When will I get my IRS tax refund?